Deterministic and Stochastic Models for the Detection of Random Constant Scanning Worms

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This paper discusses modeling and detection properties associated with the stochastic behavior of Random Constant Scanning (RCS) worms. Although these worms propagate by randomly scanning network addresses to find hosts that are susceptible to infection, traditional RCS worm models are fundamentally deterministic. A density-dependent Markov jump process model for RCS worms is presented and analyzed herein. Conditions are shown for when some stochastic properties of RCS worm propagation can be ignored and when deterministic RCS worm models can be used. A computationally simple hybrid deterministic/stochastic point-process model for locally observed scanning behavior due to the global propagation of RCS scanning worm epidemics is presented.